Understanding/plotting fixed effects estimates & standard errors

Dear all,

I have ran a mixed effects binomial model and am trying to understand how the estimates of my model relate to its conclusions. It is a fairly simple model with one fixed categorical factor (2 levels) and a nested random effect. I am using lmer and the Wald test result, the likelihood ratio test and running a similar model using MCMCglmm all seem to point in the direction that the fixed effect is significant and important. However, as I am trying to extract the estimates and their standard errors to plot the results (by running a model without the intercept or releveling the factor), it is clear that there is a huge overlap in the estimates of the two levels of the fixed effect.

In the main model (below), the standard error has a very small standard error, but the SE for the intercept is fairly large, and encompasses the estimate of the second level.

So I am trying to understand - am I interpreting something wrong? Converting them from the log-odds scale doesn't seem to help much. If not, how should I reconcile these two pieces of evidence?  Is the releveling/removing intercept approach to understand estimates from a model not valid for mixed models? 

Many thanks for any help!  below you will find the results:

m1=lmer(cbind(success,fail) ~ factor+ (1|spp/variable), bb, family='binomial')

summary(m1)

Generalized linear mixed model fit by the Laplace approximation 
Formula: cbind(success, fail) ~ factor + (1 | spp/variable) 
   Data: bb 
   AIC   BIC logLik deviance
 166.8 173.8 -79.41    158.8
Random effects:
 Groups       Name        Variance Std.Dev.
 variable:spp (Intercept) 0.014916 0.12213 
 spp          (Intercept) 1.907228 1.38102 
Number of obs: 42, groups: variable:spp, 42; spp, 7

Fixed effects:
            Estimate Std. Error z value Pr(>|z|)    
(Intercept)  1.43834    0.52289   2.751  0.00595 ** 
factor1      0.21081    0.04269   4.938 7.88e-07 ***
---
Signif. codes:  0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1 

Correlation of Fixed Effects:
       (Intr)
factor1 -0.040

m0=lmer(cbind(success,fail) ~ 1+ (1|spp/variable), bb, family='binomial')

anova(m0,m1)

Data: bb
Models:
m0: cbind(success, fail) ~ 1 + (1 | spp/variable)
m1: cbind(success, fail) ~ factor + (1 | spp/variable)
   Df    AIC    BIC  logLik  Chisq Chi Df Pr(>Chisq)    
m0  3 183.16 188.37 -88.579                             
m1  4 166.81 173.76 -79.406 18.346      1  1.842e-05 ***
---
Signif. codes:  0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1

m3=lmer(cbind(success,fail) ~ factor-1+ (1|spp/variable), bb, family='binomial')

summary(m3)

Generalized linear mixed model fit by the Laplace approximation 
Formula: cbind(success, fail) ~ factor - 1 + (1 | spp/variable) 
   Data: bb 
   AIC   BIC logLik deviance
 166.8 173.8 -79.41    158.8
Random effects:
 Groups       Name        Variance Std.Dev.
 variable:spp (Intercept) 0.014916 0.12213 
 spp          (Intercept) 1.907221 1.38102 
Number of obs: 42, groups: variable:spp, 42; spp, 7

Fixed effects:
       Estimate Std. Error z value Pr(>|z|)   
factor0    1.4383     0.5229   2.751  0.00595 **
factor1    1.6491     0.5229   3.154  0.00161 **
---
Signif. codes:  0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1 

Correlation of Fixed Effects:
       factor0
factor1 0.997

Abra?os,
Rafael Maia
---
webpage: http://gozips.uakron.edu/~rm72
"A little learning is a dangerous thing; drink deep, or taste not the Pierian spring." (A. Pope)
Graduate Student - Integrated Bioscience
University of Akron
http://gozips.uakron.edu/~shawkey/